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Irreducible representations of Hecke-Kiselman monoids
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NSTL
Elsevier
Let K[HK Theta] denote the Hecke-Kiselman algebra of a finite oriented graph Theta over an algebraically closed field K. All irreducible representations, and the corresponding maximal ideals of K[HK Theta], are characterized in case this algebra satisfies a polynomial identity. The latter condition corresponds to a simple condition that can be expressed in terms of the graph Theta. The result shows a surprising similarity to the classical results on representations of finite semigroups; namely every representation either comes form an idempotent in the Hecke-Kiselman monoid HK Theta(and hence it is 1-dimensional), or it comes from certain semigroup of matrix type. The case when Theta is an oriented cycle plays a crucial role; the prime spectrum of K[HK Theta] is completely characterized in this case. (C) 2022 Elsevier Inc. All rights reserved.
Hecke-Kiselman algebraMonoidIrreducible representationsAlgebra of matrix typePrime ideals
NSTL
Elsevier
